1) The document presents a study on modeling and control of a conical tank level process, which is a non-linear, time-varying system. 2) A mathematical model is developed for the conical tank and the process is divided into three linear regions. A conventional PI controller is designed for each region using Ziegler-Nichols tuning. 3) To overcome the limitations of the PI controller for the non-linear system, a PSO-based neural network internal model controller (NNIMC) is designed. Simulation results show that the PSO-based NNIMC provides better performance than the NNIMC and PI controller in terms of errors and settling time.